My favorite homebrew apps are:-WiiXplorer because of its text editor, image viewer, music player, file browser, app and channel launcherand FTP to wirelessly transfer files to and from wii storage devices.-GeckoOS for cheats in wii games-WiiMC, a sweet-looking media player.-Riivolution which can install non-permanent mods to games. Such mods can be language translations, texture hacks, custom levels, etc..-Priiloader to entirely skip over Nintendo's system menu on boot and through the home button. You'll have the homebrew channel and several methods to launch channels so why bother with the system menu anymore? Not much reason except to change system settings but you generally set things up once and leave it.-Wii64, SNES 9x GX, FCEUGX, VBAGX and Genesis Plus GX. An N64, SNES, NES, GBA/GBC/GB and Sega Genesis emulator respectively.

He is specifically asking for homebrew that can be installed, not just launched from SD card. Most homebrew cannot be installed as it can be very dangerous to install files to the Wiis filesystem and it's not required for most cases. I'm not sure why you are interested in homebrew that can be installed, but the top 3 homebrew that come into my mind are the homebrew channel, bootmii and perhaps priiloader.